Global Banking and the Conduct of Macroprudential Policy in a Monetary Union

(1)

Munich Personal RePEc Archive

Global Banking and the Conduct of Macroprudential Policy in a Monetary Union

Poutineau, Jean-Christophe and Vermandel, Gauthier

Université of Rennes 1, Paris-Dauphine and PSL Research Universities, France Stratégie

1 November 2016

Online at https://mpra.ub.uni-muenchen.de/81367/

MPRA Paper No. 81367, posted 16 Sep 2017 09:02 UTC

(2)

Global Banking and the Conduct of Macroprudential Policy in a Monetary Union

Jean-Christophe Poutineau^a and Gauthier Vermandel^∗,b,c

aCREM, UMR CNRS 6211, Universit´e de Rennes I, France.

bParis-Dauphine and PSL Research Universities, France

cFrance Strat´egie, Services du Premier Ministre, France

2017

Abstract

This paper questions the role of cross-border lending in the definition of national macroprudential policies in the European Monetary Union. We build and estimate a two-country DSGE model with corporate and interbank cross-border loans, Core-Periphery diverging financial cycles and a national implementation of coordinated macroprudential measures based on Countercyclical Capital Buffers. We get three main results. First, targeting a national credit-to-GDP ratio should be favored to federal averages as this rule induces better stabilizing performances in front of important divergences in credit cycles between core and peripheral countries. Second, policies reacting to the evolution of national credit supply should be favored as the transmission channel of macroprudential policy directly impacts the marginal cost of loan production and, by so, financial intermediaries. Third, the interest of lifting up macroprudential policymaking to the supra-national level remains questionable for admissible value of international lending between Eurozone countries. Indeed, national capital buffers reacting to the union-wide loan-to-GDP ratio only lead to the same stabilization results than the one obtained under the national reaction if cross-border lending reaches 45%. However, even if cross-border linkages are high enough to justify the implementation of a federal adjusted solution, the reaction to national lending conditions remains remarkably optimal.

JEL classification: F42; F45; E58; F34.

Keywords: Macroprudential Policy; Global Banking; International Business Cycles; Euro Area.

We are very grateful to the editors and three anonymous referees for their helpful comments that helped us to improve significantly the paper. We thank Taryk Bennani, Ambrogio Cesa-Bianchi, Jean-Bernard Chatelain, Laurent Clerc, Patrick F`eve, Julien Idier, Christoffer Kok, John Lewis, Pier Lopez, Marco Ratto, Karl Walentin and Raf Wouters for their comments. We are grateful to Johannes Pfeifer for providing codes for optimal policy rules with restrictions. We thank Jean-Pierre Allegret, Manuel Mota Freitas Martins and Tovonony Razafindrabe for their discussions as well as participants at the conference in International Macroeconomics in Paris, the Conference in Computational Economics, the International Symposium in Money Credit and Banking in Lyon, the French Economic Association annual meeting in Lyon and seminars at the Bank of England and the Banque de France. This paper was written while Gauthier Vermandel was working for European Central Bank, DG Macroprudential Policy and Financial Stability, Macro-Financial Linkages Division. We remain responsible for any errors and omissions.

∗Corresponding author: gauthier@vermandel.fr

(3)

1 Introduction

The disruption of financial relations that followed the 2007 subprime crisis set the basis for the adoption of macroprudential policies in most countries.¹ In the Euro Area, the implementation of such measures remains fragmented along national lines while the coordination and internal- ization of cross-border spillovers are achieved through the actions of the European Systemic Risk Board (ESRB, henceforth). This federal organization accounts for two conflicting features of the Eurozone that can be approached by contrasting core and peripheral countries.² Panel (a) of Figure 1 shows that financial cycles (as measured by the credit to GDP ratio in percentage deviation from HP trend) remain clearly national, which militates for a decentralized definition and implementation of macroprudential measures. However, as reported in panel (b) ofFigure 1, these two regions are closely linked by cross-border banking activities (as measured by the share of loans lent to a foreign agent residing in another Euro Area country) and the international spillovers of national macroprudential policies may be harmful for the monetary union. The remaining uncertainties on undesirable side-effects of self oriented macroprudential policies have thus put global banks at a central stage in the on-going debate related to the conduct of macroprudential policies.³

2000 2003 2006 2008 2011

−^{5 %} 0 % 5 %

Credit-to-GDP

% deviation from HP Trend

2003 2004 2006 2007 2008 2010 2011 2012 6 %

8 % 10 % 12 % 14 %

Share of Cross-Border Loans in Banks’ Balance Sheet

Core countries Peripheral countries

Note: Cross-border lending refers to any financing arrangement that crosses national borders between a domestic bank and a foreign borrower. The share of cross-border loans is computed here as the ratio between loans to euro area excluding the domestic area and the loans to euro area (i.e. cross-border loans between core countries are included in the calculation of the share of international loans). Sources: ESRB and ECB statistics.

Figure 1: Stylized facts characterizing the Eurosystem banking system: credit cycles remain clearly national while cross-border lending experienced an important growth

This paper questions how sizable cross-border lending flows should be treated in the definition of national macroprudential policies in the Euro Area. We more particularly assess whether cross-border bank lending should explicitly be considered in the setting of coordinated national macroprudential measures or whether national regulators should only focus on the sole national financial stance to contribute to the financial stability of the Eurozone.

We build and estimate a two-country DSGE model that accounts for two major aspects to address the question at hands. First, we extend the setup ofPoutineau and Vermandel (2015)

1In a nutshell, macroprudential policy aims at completing monetary policy to enhance the resilience of the financial system and contain the procyclicality of financial factors on activity.

2In the first group we aggregate data for countries with a current account surplus and low government bond yields over the sample period (Austria, Belgium, Germany, Finland, France, Luxembourg and Netherlands), while in the second group, we aggregate data for countries with a current account deficit and high government bond yields over the sample period (Spain, Greece, Ireland, Italy and Portugal).

3For example, regarding issues related to macroprudential policy with global banking, we refer to the IMF (2013, key issues, p31), the ESRB handbook(2014), ECB (2015, Financial Stability Review, May), Bank of England (2015, Staff Working Paper).

(4)

- featuring cross-border banking on the corporate and interbank loan markets⁴ - to account for bank capital regulation and thus to contrast the effectiveness of macroprudential policy from banking autarky to perfect integration. Second, in line with the actual organization of macroprudential policy,⁵ we focus on the joint-optimization of macroprudential policy rules in each country using the countercyclical capital buffer (CCB, henceforth) rate as an instrument.

This solution has become one of the leading facets of prudential regulation since the adoption of Basel III accords(2010) by building up a bank capital buffer during periods of excessive credit growth that can be released when systemic risks abate. The international dimension of banks offered by our setting allows us to contrast different CCB rules based on: (i) the federal or the national credit-to-gdp targeting, (ii) the loan demand (from firms) or supply (from banks) to GDP targeting, and (iii) the loan inflows-to-GDP ratio targeting as envisaged by Rey(2015).

The methodology employed in this paper comprises three steps. First, we build and estimate a two-country DSGE model for the Euro Area with only monetary policy (as there are no observations for an estimation of a macroprudential rule). Second, we compute the optimal policy rules (both monetary and macroprudential policy) given the estimated parameters assuming a two-stage game where monetary policy is the leader.⁶ Third, we examine implications of cross-border lending on the optimal design of macroprudential rules across country members of the Eurosystem using the optimal monetary policy rule as a benchmark.

The main result of the paper suggests that self oriented macroprudential national policies reacting to the evolution of home country loan creation should be favored even with high amounts of cross-border lending flows: First, targeting a national credit-to-gdp ratio should be favored to federal averages as this rule induces better stabilizing performances in front of important divergences in credit cycles between core and peripheral countries. Second, policies reacting to the evolution of national credit supply should be favored as the transmission channel of macroprudential policy directly impacts the marginal cost of loan production and, by so, financial intermediaries. Third, the interest of lifting up macroprudential policymaking to the supra-national level remains questionable for admissible value of international lending between Eurozone countries. Indeed, national capital buffers reacting to the union-wide loan-to-GDP ratio only lead to the same stabilization results than the one obtained under the national reaction if cross-border lending reaches 45%. However, even if cross-border linkages are high enough to justify the implementation of a federal adjusted solution, the reaction to national lending conditions remains remarkably optimal.

Additionally, we outline some particularities regarding the conduct of macroprudential policies for peripheral countries. We find that adjusting the macroprudential instrument to capital inflows-to-GDP is a promising tool for these countries that have experienced a large amount of loan inflows. Furthermore, disentangling the demand/supply of credit has implications for macroprudential policymaking as it is preferable to target credit suppliers for core countries and borrowers for peripheral economies.

Our approach is partly related to a set of papers examining macroprudential measures in the Eurozone with a closed economy setup. Notably, Darracq-Pari`es et al.(2011) andAngelini et al. (2014) build a DSGE model of the Eurozone close to Gerali et al. (2010) with both corporate and housing credit markets and evaluate the optimal mix between monetary and

4In this paper, we omit the mortgage market and concentrate on corporate and interbank loans. Given the insignificant size of cross-border housing loans in the portfolio of banks (the share of cross-border loans is below 1% in the Euro Area according to ECB internal data), this omission does not seem to be important for the analysis conducted here.

5We refer to Carboni et al. (2013) for a discussion regarding the macroprudential policy mandate in the Euro Area shared between European Central Bank and the Single Supervisory Mechanism, national competent authorities and coordinated by the European Systemic Risk Board.

6A important branch of the literature analyzed the interaction between monetary policy and financial stability, a topic not covered in the paper as we concentrate here on interactions between national prudential authorities.

We refer to Woodford(2012) for a summary of policy challenges and results offered by the existing literature concerning the role of monetary policy in providing financial stability.

(5)

macroprudential policy using loss functions. As a key contribution to the literature, they suggest that time-varying capital requirements can improve macroeconomic stability by supporting monetary policy actions. Our analysis can thus be considered as an extension to these papers, by accounting for the heterogeneity between Euro Area participants and the existence of national macroprudential policies with cross-border spillovers.

Our paper also contributes to macroprudential policy analysis in open economies. As an example, Quint and Rabanal (2014) account for financial asymmetries between participating countries and focus on the interaction between financial and housing cycles without considering cross-border flows between countries. By omitting cross-border lending, they naturally find that there are no important spillover effects of regulation from one member state to another via an estimated two-country DSGE model of the Eurozone. Additionally, Jeanne (2014) employs a static open economy model to evaluate the effectiveness of macroprudential and capital control measures. Contrary to Quint and Rabanal (2014), he finds that these prudential policies generate important global spillovers even with international coordination.

The paper is organized as follows: Section 2 describes the financial sector of the model.

Section 3 takes the model to the data. Section 4discusses the performance of macroprudential policy. Section 5provides a sensitivity analysis to assess the robustness of our results. Section 6 concludes.

2 The financial sector

The economy is composed of two countries of unequal size and populated by households, firms and banks. This first section describes the banking component of the model while the rest of the framework (standard to the literature) is presented in appendix.

2.1 The financial sector in a nutshell

Figure 2 provides a broad picture of the financial sector and summarizes its interaction with the rest of the economy. Banks engage in interbank lending/borrowing relations and provide corporate loans to entrepreneurs and deposit services to households. Authorities affect the decisions of the banking sector through monetary and macroprudential policies.

Monetary Policy Macroprudential

Policy

Macroprudential Policy

Bank

Production

Household

Household Cc,t

Cp,t

L^s_c,t

L^s_p,t

Investment Flows

Consumption Flows Corporate

Credit Flows Interbank

Credit Flows Refinancing

RateRt

νc,tcapital buffers

νp,t capital buffers

DepositsD^d_c,t

DepositsD^dp,t

Figure 2: Macroprudential policy and cross-border banking in a New Keynesian Framework To introduce an interbank market, we assume that banks are heterogenous in terms of liquidity. This feature gives rise to an interbank market where liquid banks provide interbank

(6)

loans to both home and foreign banks. This feature is line with the current European banking system characterized by banks relying on wholesale fundings as illustrated by Giannone et al.

(2012). In our setup, the distinction between liquid and illiquid banks lies in the direct access of liquid banks to ECB fundings which allow intra-financial sector flows between financial intermediaries.⁷ Extending this assumption to an international perspective, illiquid banks can borrow from both domestic and foreign liquid banks, which gives rise to cross-border interbank lending flows. The decision of the banking system regarding the provision of deposit services to households and loans to the corporate sector affects the rest of the economy through the setting of deposit and lending interest rates.⁸ In line with the EMU situation, we do not consider cross-border deposit nor cross-border lending to households. The international flow of loans between economies is thus a consequence of interbank liquidity provision and borrowing choices undertaken by entrepreneurs (following a comparison between the relative interest rates of domestic and foreign corporate loans).

This paper adopts a macroeconomic perspective to focus on the effect of cross-border lending on the conduct of macroprudential policy in a heterogeneous monetary union. As a consequence, the financial sector is combined with a standard two-country DSGE model accounting for short run rigidities in goods prices and nominal wages. In what follows, we outline the main assumptions regarding the functioning of the financial sector that are deemed necessary to improve both the tractability of the analysis and the estimation of the many behavioral parameters of the DSGE structure. Some modelling choices have been done in line with the DSGE literature that contrast with a more standard description of the behavior of the banking sector as sum- marized byFreixas and Rochet (2008) andVanHoose (2009). As in the initial contribution of Gerali et al. (2010), this macro superstructure is augmented with a highly simplified banking model. A host of assumptions should be invoked that effectively splinter a bank’s decisions into independent choices about different portions of its balance sheet.⁹

This paper extendsPoutineau and Vermandel(2015) to account for deposit decisions and for macroprudential consideration in the balance sheets of financial intermediaries. The stickiness in both deposit and loan interest rates is a key ingredient of the framework. The setting of interest rate mimics the way other sticky nominal variables such as prices and wages are set in the model by adopting a Calvo-type mechanism. This device, shared by most DSGE models with a banking sector, partly contrasts with the literature developed from the banking indus- try perspective. Indeed, most of the banking literature has, following Flannery(1982) original work on deposits as quasi-fixed factors, focused on intertemporal quantity adjustment costs. It is also worth noting that the substantial banking literature on this topic has proposed alterna- tive ways of approaching this question, including Cosimano and Van Huyck(1989), Cosimano (1987,1988), andElyasiani et al. (1995) andAbo-Zaid(2015). Furthermore, sluggish and even asymmetric variations in bank retail rates have been documented in the empirical literature as

7This assumption is empirically motivated: in the Eurosystem, only a fraction of the 2500 banks participates regularly to the bidding process in main refinancing operations of the ECB while the others rely on interbank funding.

8For tractability reasons we assume that even if banks differ in their ability to raise funds from the central bank, their loan and deposit supply decisions remain homogenous after aggregation. In a real life situation, illiquid banks may face more difficulties in attracting households deposits requiring banks to set higher deposit rates to compensate their default risk. Regarding corproate loans provision, the tighter funding constraint of illiquid may diminish their loan supply compared to liquid banks.

9First, portfolio separation holds (Baltensperger (1980) and Santomero (1984)), which means (Sealey and Lindley(1977) andSealey(1985)) that a number of assumptions have been invoked. For instance, either shareholder unanimity is assumed for all banks in the model, or risk neutrality has been assumed to render shareholder unanimity a non-issue. In addition, it must be assumed that banks’ costs of real resources utilized in their operations are separable from resource costs for others of the banks’ assets and liabilities at during each period and across periods if interperiod adjustment costs are taken into account. Finally, banks must have access to a market in which they can both borrow and lend at exactly the same interest rate. Only when all such assumptions are invoked, it is legitimate for each bank to be able to make separable decisions about balance-sheet choices as assumed in this model.

(7)

inVan Leuvensteijn et al.(2013) through imperfect competition among banking systems, while Kopecky and Van Hoose (2012) rely on intertemporal quantity adjustment costs together with imperfect competition to explain such observations. The adoption of a Calvo mechanism combined with monopolistic competition has been employed here in a macro-perspective for credit and deposit interest rates, as this solution allows us to consider the sluggishness in the adjustment of all the nominal variables of the economy (prices, wages and interest rates) through the estimation of a ”Calvo lottery parameter”.

As a second major noticeable difference from Poutineau and Vermandel(2015), we account for endogenous leverage of financial intermediaries, thus reflecting the riskiness in the balance sheet of banks. We use time-varying capital requirements as the macroprudential instrument.

As underlined byAngelini et al.(2014), capital buffers have taken a center stage in the ongoing debate on regulatory reform and have become one of leading facet of macroprudential regulation. Specifically in the European Union, a number of macro-prudential policy instruments including countercyclical buffers are embedded in the legislative texts transposing the Basel III regulatory standards into EU law.¹⁰ To account for this compulsory macroprudential instrument, we borrow the modelling device ofDarracq-Pari`es et al.(2011) andAngelini et al.(2014) by assuming that each type of bank must pay a quadratic cost when its risk weighted assets ratio deviates from the time-varying ratio fixed by the macroprudential authority in country i according to the systemic risk arising within the financial system. The decision to penalize banks for keeping equity-capital positions below the official benchmark is easy to understand, as undercapitalized banks make the banking sector more fragile and in turn subject to bank runs (Diamond and Rajan (2001)). Symmetrically, the decision to impose costs on banks for having equity-capital positions above the required levels may be understood in a macroeconomic perspective: by keeping more equity capital levels than required by the official regulation, the banking sector diverts resources and, in turn, creates credit rationing for both entrepreneurs and illiquid banks. This may create lower than desired banking activity, reduce investment in the economy and incur inefficiencies.¹¹

2.2 Interbank relations

In each country the banking system consists of two distinct branches: a continuum of monopolistic banks and financial packers. Monopolistic banks provide different types of loans and deposit services and set interest rates on a Calvo basis. The financial intermediary is a CES packer that produces one homogenous loan and deposit service.¹²A shareλof banks is illiquid (i.e. credit constrained), while the remaining share of banks 1-λis liquid and supplies interbank loans to illiquid banks.

10Namely the new Capital Requirements Directive (CRD IV) and the Capital Requirements Regulation (CRR).

We refer toCarboni et al.(2013) for a discussion regarding the macroprudential policy mandate in the Euro Area shared between ECB/SSM, national competent authorities and coordinated by the ESRB.

11Van den Heuvel(2008) finds using a general equilibrium model that increasing capital requirements induces high welfare costs in terms of unconditional consumption, suggesting that capital requirements should be lower than in the current adequacy framework. Clerc et al.(2015) highlight the presence of a tradeoff using a financial accelerator model between too high and too low capital requirements.

12The financial packer acts as a loan and deposit bundler in a perfectly competitive market. Banks supply differentiated types b of deposits Di,t(b) and loans L^s_i,t(b) bundled by financial packers. Their pack- ing technology for deposit services and loans reads as, D^d_i,t = [(1/ni)^1/ǫ^DG(Di,t(b)^(ǫ^D⁻^1)/ǫ^D)]^ǫ^D^/(ǫ^D⁻¹⁾, and L^d_i,t = [(1/ni)^1/ǫ^LG(L^s_i,t(b)^(ǫ^L⁻^1)/ǫ^L)]^ǫ^L^/(ǫ^L⁻¹⁾. It maximizes profits, R^D_i,tD^d_i,t+R^L_i,tL^d_i,t− G(R^D_i,t(b)Di,t(b))− G(R^L_i,t(b)L^s_i,t(b)), subject to their two technology curves. Here, L^d_i,t is the loans demand from home and foreign entrepreneurs, D_i,t^d is the deposit services demand from domestic households and G(.) is the aggregator function. Deposits and loans are imperfect substitute with elasticity of substitutionǫD <−1 andǫL>1. The corresponding demand functions associated from the previous problem are,Di,t(b) = (1/ni)(R_i,t^D(b)/R^D_i,t)⁻^ǫ^DD_i,t^d andL^s_i,t(b) = (1/ni)(R^L_i,t(b)/R^L_i,t)⁻^ǫ^LL^d_i,t. The aggregate price index of all varieties in the economy is given by, R_i,t^D = [(1/ni)G(R^D_i,t(b)¹⁻^ǫ^D)]^1/(1⁻^ǫ^D⁾andR^L_i,t= [(1/ni)G(R^L_i,t(b)¹⁻^ǫ^L)]^1/(1⁻^ǫ^L⁾.

(8)

The representative share λof illiquid banksb in countryihas the following balance sheet, L^s_i,t =IB_i,t^H +BK_i,tîll+D_i,t+liabîll_i,t, (1) where L^s_i,t is the loan supply of borrowing banks, IB_i,t^H is the interbank loans supplied by liquid banks subject to external habits, BK_i,tîll is the bank capital, D_i,t are deposit services to households and liab_i,t are other liabilities in the balance sheet of the bank that are not considered in the model.¹³ To close the model, we assume that the cost of these liabilities is set by the central bank through its refinancing rate. We suppose that the demand for interbank funds are subject to external habits at a degree h^B_i where IB_i,t^H =IB_i,t^d −h^B_i (IB_i,t−1^d −IB^d_i).

These habits captures the empirical autocorrelation of interbank funding. In addition, these habits are empirically documented in the interbank network literature: Finger et al. (2014, 2015) find at a bank level that bilateral links between banks are persistent as banks heavily rely on well-established business relations, thus exhibiting some habits in borrowing/lending decisions.

The one-period stream of profits of the b-th illiquid bank is given by:

Π^ill_i,t =

1−µ^B(1−E_t{η_i,t+1})

1 +R^L_i,t

L^s_i,t− 1 +R^D_i,t

D_i,t− 1 +P_i,t^IB

IB_i,t^H (2)

−(1 +Rt)liab^ill_i,t−F

rwa^ill_i,t−vi,t

BK_i,t^ill,

where µ^B ∈[0,1] denotes the loss-given-default (i.e. the percentage of the amount owed on a defaulted loan that the bank is not able to recover), 1−E_t{ηi,t+1}is the expected average default rate of the bank’s home and foreign customers,¹⁴R^D_i,t is deposit rate,P_i,tÎB is the borrowing cost on the interbank, R_t the interest rate set by the central bank and F_i(·) denotes the capital requirement cost function. This cost function is taken from Gerali et al. (2010) and is defined as F_i(x) = 0.5χ^kx² where χ^k ≥ 0 is the cost of capital adequacy framework paid in term of bank capital.¹⁵ This cost function is a shortcut that makes bank capital more costly than any source of financing, and allows in turn to mimic the response of credit rates and credit to a capital requirement tightening consistently with empirical evidence (see for instance Fraisse et al.(2013) for an empirical measure of this elasticity). When the bank capital-to-risky-asset ratiorwaîll_i,tis below the policy targetυ_it, the bank is penalized by regulatory rules that affect the borrowing rates in the monetary union and in turn damage output. This penalization replicates the market discipline imposed by investors on low capitalized banks, forcing the latter to boost their retained earnings though higher credit rates. The risk is evaluated through fixed weights on assets, based on the type of the borrowers (1 for corporate exposure and 0.20 for interbank exposure between OECD banks as defined in Basel accords) as defined in Basel I accords. Since illiquid banks are only exposed to corporate risk, the risk weighted assets ratio is given by rwaîll_i,t =BK_i,tîll/L^s_i,t. In addition, the financial intermediary has access to domestic and foreign interbank loans to meet its balance sheet. The modelling device to introduce international borrowing is analogous to trade channels through a CES as inPoutineau and Vermandel(2015) andBrzoza-Brzezina et al.(2015). The total amount borrowed by the representative bank reads

13We suppose that they follow an exogenousAR(1) shock processε^B_i,tsuch that,liabi,t=e^ε^B^i,tliabi,this shock captures some aggregate movements in the funding constraint araising from the wholesale funding market, see for instanceP´erignon et al.(2017) for an analysis of liquidity runs on the French unsecured market of certificates of deposits.

14To simplify both the steady state and the log-linear version of the model, the bank default expectation regarding entrepreneurs’ projects is defined by a geometric average of home and foreign surviving rates of entrepreneurs, ηi,t= (η_h,tÊ )¹⁻^α^L^h(ηÊ_f,t)^α^L^jη¯^α^L^h⁻^α^L^j whereη_i,t+1Ê is the default rate of entrepreneurs operating in countryi∈ {c, p}.

The expression ¯η^α^L^h⁻^α^L^j ensures the detesministic steady state remains symmetric between Core and Periphery without affecting the dynamic of the model up to a first order approximation.

15The quadratic nature of this cost has been discussed in the previous subsection.

(9)

as follows:

IB_i,t^d =

1−α^IB_i 1/ξ

IB_hi,t^d (ξ−1)/ξ

+ α^IB_i 1/ξ

IB_{f i,t}^d (ξ−1)/ξξ/(ξ−1)

, (3)

where parameterξ >0 is the elasticity of substitution between domestic and foreign interbank funds, α^IB_i represents the percentage of cross-border interbank loan flows in the monetary union and IB_hi,t+1^d (resp. IB_{f i,t+1}^d ) the amount of domestic (resp. foreign) loans demanded by borrowing bank b in country i. This existence of an home bias on the interbank market is empirically motivated, Fricke and Lux (2015) find, using Italian bank-level data, that Italian banks tend to trade with each other rather than with foreign banks, in particular after the financial turmoil. More broadly in the literature of finance, the home bias in portfolio was first documented by French and Poterba(1991).

The total cost incurred by illiquid banks to finance interbank loans, 1 +P_i,t^IB, is thus defined according to the CES aggregator:

1 +P_i,t^IB = ( 1−α^IB_i

(1 +RÎB_h,t)^1−ξ+αÎB_i (1 +RÎB_f,t)^1−ξ)^1/(1−ξ), (4) where 1 +RÎB_h,t (resp. 1 +RÎB_f,t) is the cost of loans obtained from home (resp. foreign) banks in country i. Finally following Gerali et al. (2010), the bank capital accumulation process of illiquid banks (BK_i,tîll) is determined by:

BK_i,t^ill =

1−δ_i^ill

Π^ill_i,t−1, (5)

whereδ_i^ill∈[0,1] measures resources used in managing bank capital and conducting the overall banking intermediation activity and is determined endogenously by the steady state of the model. Given the functional form ofF_i(·), the first order condition on loans which determines the marginal cost of supplying an additional unit of loans to home and foreign entrepreneurs is:

1 +M C_i,t^ill=

1 +P_i,t^IB+χ^k

v_i,t−rwa^ill_i,t rwa^ill_i,t2

1−µ^B(1−E_t{η_i,t+1}) . (6)

From this equation, we observe that an increase (reduction) in the CCB rateυ_i,t (risk weighted assets ratiorwa^ill_i,t) imposes on banks to accumulate more equity via retained earnings through a rise in credit rates. Parameterχ^kdetermines the elasticity of interest rates to capital regulation change.¹⁶ During phases of expansion, banks have incentives to increase their leverage away from the target in order to boost their profits. This risk taking by banks is addressed in our model though the cost function that forces banks to control their capital structure.

The fraction 1−λof remaining liquid banks has the following balance sheet:

L^s_i,t+IB_i,t^s =L^ECB_i,t +BK_i,t^liq+Di,t+liab^liq_i,t, (7) whereL^s_i,t is the lending supply to entrepreneurs,IB_i,t^s is the supply of funds on the interbank market, L^ECB_i,t is the amount of refinancing operations obtained by the liquid bank, BK_i,t^liq is the amount of bank capital,D_i,t are deposits collected from domestic households andliab_i,t are exogenous liabilities as explained previously. The one-period profit of the bank Π^liq_i,t is defined as:

Π^liq_i,t = 1−µ^B(1−E_t{η_i,t+1})

1 +R_i,t^L

L^s_i,t+ 1 +R^IB_i,t

IB_i,t^s − 1 +R^D_i,t

D_i,t (8)

−(1 +R_t)liab^liq_i,t −(1 +R_t)L^ECB_i,t −F(rwa^liq_i,t −υ_it)BK_i,t^liq.

16Empirically, Fraisse et al.(2013) find at a bank level that one percentage increase in capital requirements leads to a reduction in lending by approximately 10%.

(10)

Here, R^IB_i,t is the interest rate set by liquid banks to home and foreign illiquid banks, R_t is the refinancing rate of the central bank and F_i(·) denotes the same Basel cost function as for illiquid banks: F_i(x) = 0.5χ^kx². Interbank claims affect the amount of equity held by banks and are given a risk weight at 20%. The risk weighted asset ratio for liquid bank incorporating corporate and bank exposures is given by rwa^liq_i,t = BK_i,t^liq/(L^s_i,t + 0.2IB_i,t^s ). According to the illiquid bank, bank capital of liquid banks evolves according to

BK_i,t^liq = (1−δ_i^liq)Π^liq_i,t−1, (9)

whereδ^liq_i ∈[0,1] is similar to the illiquid bank and measures the fraction of capital used during the intermediation process that cannot be re-invested next period. The first order condition on loans determining the marginal cost of loans of the liquid bank bis:

1 +M C_i,t^liq=

1 +Rt+χ^k

vi,t−rwa^liq_i,t rwa^liq_i,t2

1−µ^B(1−E_t{η_i,t+1}) , (10)

and the second first order condition on interbank loans determines the interbank rate set by banks operating in countryi:

R^IB_i,t =R_t+ 0.2χ^k(v_i,t−rwa^liq_i,t)(rwa^liq_i,t)². (11) Here again, an increase in bank capital requirements raises the bank’s cost of lending, and in turn increases both interbank and corporate interest rates. This result is consistent with standard business cycle models and is referred to the bank capital channel as inVan den Heuvel (2008),Meh and Moran (2010),Darracq-Pari`es et al. (2011) andAngelini et al. (2014).

2.3 Interest rate setting

We assume that interest rates on deposits and corporate credit loans are sticky. In particular, sluggish and even asymmetric variations in bank retail rates have been documented in the empirical literature as in Kopecky and Van Hoose (2012) and Van Leuvensteijn et al. (2013) through imperfect competition among banking systems. The setting of interest rate mimics the way other sticky nominal variables such as prices and wages are set in the model. As in Darracq-Pari`es et al. (2011), we introduce a Calvo model for credit rates to firms and deposit rates while the interbank rate is left flexible as banks operate under perfect competition on the interbank market. Banks must solve a two-stage problem. In the first stage, banks minimize the cost of managing their funds on a competitive input markets by computing the marginal cost of supplying an additional loan to borrowers and a deposit service to households. The computation of these marginal costs has already been performed in the previous subsection. In a second stage, they operate under monopolistic competition by applying a markup (markdown) on their commercial loan (deposit) rate, and set the interest rate on a staggered basis. Using a Calvo nominal rigidity device, each period a random fraction θ_i^L (θ^D_i ) of banks is unable to update its lending (deposit) rate, R^L_i,t =R^L_i,t−1 (R_i,t^D = R^D_i,t−1), creating an imperfect transmission of monetary policy decisions to borrowers and savers living in the monetary union. The bank that it is able to modify its loan interest rate (with a constant probability 1−θ_i^L) chooses R^L∗_i,t to maximize its expected stream of profits adjusted by the risk of default:

E_tX∞

s=0 θ^L_iτ

Λi,t+s 1−µ^B(1−ηi,t+1+τ) R_i,t^L∗−exp(ε^L_i,t+s)M C_i,t+s^L

L^s_i,t+s, (12) where ε^L_i,t is an ad-hoc markup AR(1) shock to the credit rate equation, θ^L_i ∈ [0,1) is the Calvo lottery coefficient determining the degree of nominal rigidity andM C_i,t^L is the aggregate marginal cost combining outputs from liquid and illiquid banks of countryi. We aggregate loans

(11)

from liquid and illiquid banks and their respective marginal costs before applying the markup for tractability purposes: this device is useful to compute a single Phillips curve as well as an unique credit rate for both liquid and illiquid banks. We borrow this shortcut procedure from Gerali et al.(2010) adapted in a different context, i.e. all banks belonging to a national banking system share the same marginal cost of production, reflecting the average liquidity degree of national banks: 1 +M C_i,t^L = (1 +M C_i,t^ill)^λ(1 +M C_i,t^liq)^(1−λ). In addition, the banking spread reflecting the level of financial distress is given by S_i,t^L = (1 +R^L_i,t)/(1 +Rt).

In a similar fashion for deposit rates, assuming that it is able to modify its interest rate with a constant probability 1−θ^D_i , the representative bank chooses R^D∗_i,t to maximize its expected stream of profits, by applying a markdown on the refinancing rate of the central bank Rt:

E_tX∞

τ=0 θ^D_i τ

Λ_i,t+s

R_t+sexp(ε^D_i,t+s)−R_i,t^D∗

D_i,t+s, (13)

where ε^D_i,t is an ad-hoc time-varying AR(1) markdown shock to the deposit rate equation and θ^D_i ∈[0,1) is the Calvo lottery parameter.

2.4 Macroprudential policy

Macroprudential policy affects the general equilibrium of the economy through the policy instru- mentv_i,t that contributes to the marginal cost of commercial banks’ loans. As a consequence, a macroprudential policy tightening is associated with higher lending rates, and lower bank credit growth and asset prices. We assume that the macroprudential authority sets the time-varying capital requirement ν_i,t according to:

vi,t = (1−ρ^v_i) ¯ν+ρ^v_iνi,t−1+φi(Ti,t−T¯i), (14)

where ρ^v_i ∈ [0,1) is the smoothing coefficient of the rule, T_i,t is the macroprudential target, φ_i ≥ 0 is the macroprudential weight to the target in country i and ¯T_i is the steady state of the target. In our specification, capital requirements are expected to increase when the target deviates from its steady state. The choice of the target T_i,t is a key aspect of the paper that will be discussed below.

The ESRB has developed a buffer guide to choose the CCB rate based on the credit-to-gdp gap.¹⁷ However, the global nature of the European banking system introduces many possi- bilities for the definition of the credit-to-gdp ratio taken into account by national authorities.

Indeed, the CCB rate may be adjusted to the credit supply (of banks) or the credit demand (of entrepreneurs),¹⁸ either on a national or on a federal basis. Our framework with international bank flows allows us to distinguish between five operational targets as listed inTable 1.

The first set of credit targeting rules is oriented towards the supply of credit using either a federal (1.a) or a country-specific aggregate (1.b). A macroprudential policy based on credit supply aims at stabilizing lenders by focusing more on the stabilization of financial shocks hitting lenders rather than demand and supply shocks hitting borrowers. Given the scale of cross-border loans in the Eurozone, the decisions of the national supervisor has side effects on countries where a national bank has a subsidiary or branches or where this bank lends to may favor a federal definition of the ratio. Thus to handle these pecuniary externalities, we evaluate the possibility of an union-wide targeting system (1.a) against a national targeting system (1.b), the latter being expected to create more externalities (positive or negative) as it affects the foreign banking system without taking into account its financial developments.¹⁹

17Other indicators (such as early warning variables) are included in the CCB guide which are not implementable in our model.

18In an open economy context where banks can lend across borders, banks supply credit to both home and foreign, which creates a gap between the domestic supply and the domestic demand for loans. This distinction between demand and supply is easy to see on the market clearing conditions of interbank (Equation 40) and corporate markets (39).

19For further discussions of these cross-border issues, we refer toBeck et al.(2016).

(12)

Table 1

Various Macroprudential Policy Schemes in terms of Target (average in the monetary union, national supply or national target) and in terms of policy stance (common or national-adjusted)

Schemes Target

Loan Supply Targeting

1.a Union-wide loan supply Tt= (L^st+ (1−λ)IB^st)/Yt

1.b National loan supply Ti,t= (L^s_i,t+ (1−λ)IB^s_i,t)/Yi,tfori∈ {c, p}

Loan Demand Targeting

2.a Union-wide loan demand Tt= (L^d_t+λIB^d_t)/Yt

2.b National loan demand Ti,t= (L^d_i,t+λIB_i,t^d )/Yi,tfori∈ {c, p}

Capital Inflows Targeting

3 Capital Inflows Ti,t= (L^d_i,t−L^s_i,t+λIB^d_i,t−(1−λ)IB_i,t^s )/Yi,tfori∈ {c, p}

Note: variables without country subscript such asxt denote union-wide averages computed as a weighted sum of each countryxt=nxc,t+ (1−n)xp,t.

The second set of credit targeting rules concentrates on the demand of credit emanating from entrepreneurs.²⁰ The interest of a CCB rate tailored to borrowers is that it may provide more stabilization following real and nominal shocks hitting households and firms at the ex- pense of financial shocks affecting banks. This solution seeks at internalizing the social cost of entrepreneurs’ over-borrowing that may arise given their biased expectations. As this policy regime inefficiently affects foreign borrowers through cross-border lending, spillovers effects may be dampened by a federal targeting (2.a) rather than a national one (2.b).

We also evaluate the interest of adopting provisional measures to affect cross border lending directly, through targeting capital inflows in the CCB. This solution, as envisaged by Jeanne and Korinek(2010),Brunnermeier et al.(2012) andRey(2015), is relatively similar to a capital control measure. The main insight behind this scheme would rely on the fact that persistent capital account imbalances induce financial stability risks and may have implications for the sustainability of net external asset positions. In particular since the creation in the Eurozone, global banking has experienced an explosive growth helping to fuel unsustainable credit booms in peripheral economies such as in Spain and in Ireland, followed by a sudden stop in capital inflows compensated by unconventional measures. Macroprudential policies can play a key role to contain this problem by imposing targeted regulations on banks engaged in cross-border activities. When borrowing to other European banks is increasing faster with respect to the GDP, a national authority can rise the CCB rate to affect banks’ balance sheet management and reduce their exposure to international borrowing. In addition when system risks abate in one economy, leading to capital flow reversals, national authorities may release the buffer thus loosening the banks’ funding constraint to address the procyclicality of capital flows.

3 Estimation strategy

We fit the previous two country DSGE to Eurozone data over the sample time period 1999Q1- 2013Q4 using Bayesian techniques. We estimate structural parameters and the sequence of shocks by following the seminal contributions ofSmets and Wouters(2003,2007) andChristiano

20A loan demand targeting is feasible in a real life situation, the ECB already disentangles the credit demand and supply by collecting the domestic and cross-border positions of Euro area monetary financial institutions since 1999 for each participant of the monetary union. Regarding the demand side of credit markets, the bank lending survey published by the ECB on a quarterly basis provides an analysis of the driving forces of the demand of credit in the Euro Area. For the supply side, both the ECB and the BIS collect domestic and cross-border positions of euro area monetary financial institutions.

(13)

et al. (2005). For a detailed description, we refer to the original papers.

3.1 Data

We split the Eurozone in two groups adopting the core-periphery dichotomy as in Quint and Rabanal(2014) andPoutineau and Vermandel(2015). Core countries gather Austria, Belgium, Germany, Finland, France, Luxembourg and Netherlands while peripheral countries include Spain, Greece, Ireland, Italy and Portugal. The model is estimated with Bayesian methods on Eurozone quarterly data over the sample period 1999Q1 to 2013Q4, which makes 60 observations for each observable variable. Concerning the transformation of series, the point is to map non- stationary data to a stationary model. Data which are known to have a trend (namely GDP, consumption, investment, corporate loan and interbank supply) or unit root are made stationary in two steps. First, we divide the sample by the population. Second, data are taken in logs and we use a first difference filtering to obtain growth rates. In addition, real variables are deflated by the HICP price index and we remove the seasonal component in the data using a multiplicative decomposition. Furthermore, we demean the data as we do not use the information contained in the observable mean. Interest rates are set on a quarterly basis by dividing them by 4.

Since hours worked are not observable for the Euro Area, we adopt the same modelling strategy as Smets and Wouters (2003) to identify TFP shocks using employment as a proxy for hours worked. Employment is divided by the working population index, taken in logs and demeaned.

To map employment to hours worked in our model, we introduce an auxiliary equation for each country which states that only a shareθ^E_i ∈[0,1) of firms is allowed to adjust its level of employment ˆei,t to its optimal labor demandH_i,t^d:

ˆ

e_i,t=βˆe_i,t+1+ 1−βθ_i^E

1−θ^E_i /θ_i^E

log

H_i,t^d/H¯^d

−eˆ_i,t

. (15)

The vector of observable variables reads as:

Y_t= 100[∆ˆy_i,t,eˆ_i,t,∆ˆc_i,t,∆ˆı_i,t,πˆ_i,t^C,∆ ˆw_i,t,rˆ^D_i,t,∆ˆl^s_i,t,∆ibb^s_i,t,rˆ_t] fori={c, p}.

3.2 Calibration, priors and model assumptions

We fix a small number of parameters commonly used in the literature of real business cycles models which are weakly identified. The discount factor β is set at 0.99, the depreciation rate δ at 0.025, the capital share α at 0.38, the share of steady state hours worked ¯H at 1, the spending to GDP ratio g at 24%.²¹ Concerning ǫ_P and ǫ_W (the substitutability between final goods and labor), we consider the calibration at 10 as inSmets and Wouters(2007). Regarding financial parameters, we fix ¯N /K¯ (the net worth to capital) ratio to 0.40 to be consistent with the observed debt-to-financial assets ratio of non-financial corporations which fluctuates between 50% and 65% since 1999. The steady state value of spreads and the bank balance sheet are calibrated on their averages observed over the sample period in the Euro Area: ¯R- R¯^D=1.66/400, ¯R^L- ¯R^D=3.67/400, ¯D/L¯^s=0.46, rwa=¯v=0.10 and IB^d/L¯^s=0.20. The capital regulation cost χ^k is set at 11 as in Gerali et al. (2010) to replicate the response of credit and interest rate to a capital requirement rise.

For substitution parameters for corporate and interbank loans υ and ξ as well as for the fraction of illiquid banks λ, to our knowledge there are no empirical analysis using bank level data that provides an estimation of these parameters. We rely on the previous fit exercise of Poutineau and Vermandel (2015) by calibrating λ at 0.38 and υ, ξ at 1.1. The latter calibration for substitution parameters is rather conservative by allowing very low substitution effects

21This calibration offers a consumption-to-output ratio of 55.45% (vs 57.31% in the data) and investment-to- output ratio of 20.55% (vs 20.70% in the data).

(14)

between home and foreign loans.²² The quarterly share of defaulting firms’ projects 1−η¯^E is fixed at 0.025/4,²³and the auditing costµ^B at 0.10,²⁴those values are very similar toBernanke et al.(1999). We compute the parameter governing the relative size of the core area n at 0.58 as in Kolasa (2009), which is the share implied by nominal GDP levels averaged over the period 1999-2013. We calibrate symmetrically the adjustment cost on deposits χ^D_i at 0.0007 as in Schmitt-Groh´e and Uribe (2003) to remove an unit root component generated by the two- country set-up. Finally, the lower bound ω_min and the shape κ of the Pareto distribution are endogenously determined by the model equations assuming a risk-free economy with no spread and default, we obtain: ω_min=1- ¯N /K¯ and κ= ¯K/N¯. Our calibration delivers for the main endogenous variables the following steady state: ¯ω^C=0.6015,ε^D=-2.41, ε^L=4.37, ¯r^L=0.0192 and

¯

r^K=0.0166.

Our priors are listed inTable 7. Overall, they are either relatively uninformative or consistent with earlier contributions to Bayesian estimations. For a majority of new Keynesian models’

parameters,i.e. σ^L_i ,h^C_i ,θ^P_i ,ξ_i^P,θ^W_i ,ξ_i^W,θ_i^E,χ^I_i,ψ_i,φ^π,φ^∆y and shock processes parameters, we use the prior distributions close to Smets and Wouters (2003, 2007). Calvo probabilities for rates have the same uninformative priors as for prices/wages while loans habits are given a prior mean 0.5 with standard deviation 0.2. Our priors for openness parameters are based on their observed average over the sample period. Substitutabilities between home/foreign credit and final goods are set to 2 with standard deviations of 0.50. We set the prior for the elasticity of the external finance premium κ_i to a beta distribution with prior mean equal to 0.05 and standard deviation 0.02 consistent with prior information of Gilchrist et al.(2009). Finally, in order to catch up the correlation and co-movements between countries’ aggregates, we estimate the cross-country correlation between structural shocks, associated priors are inspired by in Jondeau et al. (2006) and Kolasa (2009), we set the mean of the prior distribution for shock correlations between core countries and peripheral countries at 0.2 with a standard deviation at 0.2.

Finally, regarding bank capital regulation for the fit exercise, we disable the macroprudential instrument by fixing the CCB rate to its deterministic steady state value:

νi,t = ¯v. (16)

This assumption is reasonable for two main reasons. First over the sample period, capital regulation has been mainly dominated by the Basel I Accords characterized by fixed capital requirement ratios. Second, even through the adoption of the Basel III Accords allows Euro Area countries to employ the countercyclical capital buffer as a shield against the build up of financial imbalances, it has not been yet employed by a participant of the monetary union.²⁵

22In contrast,Brzoza-Brzezina et al.(2015) assign a value of 6 to their substitution parameter, which is rather high with respect to the literature of trade. In general, substitution parameters for goods market are rather low and usually remain between 1 and 2 as inQuint and Rabanal(2014) orPoutineau and Vermandel(2015).

23This is consistent with corporate default statistics from Moody’s, the rating agency, which show an average default rate on (non-US) non-financial corporate bonds of 0.75% for the period 1989-2009, as shown byDarracq- Pari`es et al.(2011). The other rating agency Standards & Poor’s evaluates the rate of default for the period 1991-2014 to 0.58%. We consider a default rate of 0.63% which is in the ballpark of the numbers found by rating agencies.

24The auditing cost cannot be observed as few data on loan losses are publicly available for reasons of confi- dentiality.Dermine and De Carvalho(2006) find using bank level data that these costs critically depends on the size of the loans: recovery costs on smaller loans are substantially higher than on large loans, 4.1% vs. 0.9%. In addition, once the contentious department has to rely on external lawyers, the recovery costs rise to 10.4%.

25The ESRB offers on its website an interactive map of the Euro Area on countercyclical capital buffers. To this date, only Sweden and Norway have activated the CCB rate in the European Union but both of these countries are not Euro Area participants.